Proof (2005 film)

Proof is a 2005 film about Catherine, a mathematician who allows Hal, a PhD student, to go through her recently deceased father's papers, a Field Medal winner who had gone insane. Hal finds a mathematical proof to a problem that has eluded mathematicians for years - however, Catherine insists that she wrote it, and neither she nor Hal know whether she's telling the truth or succumbing to the same dementia of her father.

Contents

Just because I'm paranoid doesn't mean there isn't something in that backpack!

I really don't need this, Claire. I'm fine, you know, I'm totally fine, and then you show up here with these questions like "Are you ok?" with that soothing tone of voice and "Oh, the poor policemen", I mean, I think the policemen can handle themselves. And bagels and bananas and jojuba, and "Come to New York!" and vegetarian chili?! I mean, it really pisses me off, so just save it!

Wow, I can't believe how many people are here, I never knew he had this many friends. Where have you all been for the last five years? I guess to you guys he was already dead, right? I mean, what's a great man without his greatness? Just some old guy... So, you probably want to catch up on what you missed out on. Um, he used to read all day, he kept demanding more and more books, I was getting them out of the library by the car load, there were hundreds. And then, one day, I realised, he wasn't reading: he believed aliens were sending him messages through the dewey decimal numbers in the library books. He was trying to work out the code. He used to, um, shuffle around in his slippers, he talked to himself. He stank. I had to make sure he bathed, which... was embarrassing. Oh, and then he started writing, nineteen, twenty hours a day, I got him this huge case of notebooks, he used every one. I dropped out of school. You see, he was convinced that he was writing the most beautiful, elegant proofs. Proofs, like music. I'm glad he's dead.

[Reading Robert's notebook] "Let X equal the quantity of all quantities of X. Let X equal the cold. It is cold in December. The months of cold equal November through February. There are four months of cold, and four of heat, leaving four months of indeterminate temperature. In February it snows. In March the lake is a lake of ice. In September the students come back and the bookstores are full. Let X equal the month of full bookstores. The number of books approaches infinity as the number of months of cold approaches four. I will never be as cold now as I will in the future. The future of cold is infinite. The future of heat is the future of cold. The bookstores are infinite and so are never full except in September..."

I feel like I could crack open, like an egg, or one of those really smelly French cheeses that ooze out everywhere when you cut them.

[Referring to proof] It is forty pages long. I didn't memorize it. It is not a muffin recipe!

I didn't show this to anyone. I wanted you to be the first to see it, I didn't know I wanted that until last night. I trusted you. Was I wrong?

[If Catherine had written the proof] It would be a real disaster for you, wouldn't it? You and the other geeks who barely finish their PhDs, who are marking time doing lame research, bragging about the conferences they go to, wow. Playing in an awful band, and whining that they're intellectually past it at 26, because they ARE!

You think you've figured something out? You run over here all pleased with yourself because you changed your mind, now you're certain? You don't know anything! The book, the math, the dates, the writing, all that stuff you just decided with your buddies, it's just evidence, it doesn't prove anything!

[voiceover] How many days have I lost? How can I get back to the place where I started? I'm outside a house, trying to find my way in, but it's locked and the blinds are down, and I've lost the key, and I can't remember what the rooms look like or where I put anything. And if I dare go inside, I wonder, will I ever be able to find my way out?

[On writing the proof] It was like, connecting dots. Some nights, I, I could connect, three or four of them, and some nights they'd be really far apart, I'd have no idea how to get to the next one, if there was the next one.

[voiceover] If I go back to the beginning, I could start it over again. I could go line by line, try and find a shorter way. I could try to make it... better.

...

Robert: What about Clare?

Catherine: She's not my friend, she's my sister.

Catherine: Don't you have a job?

Hal: Yes, I have a full teaching in this quarter, plus my own work.

Catherine: Plus, band practice.

Hal: Plus I teach hockey to ten year olds twice a week.

Catherine: Ugh, you make me sick.

Claire: You will come?

Catherine: Yeah, sure, in January? I mean, it's not like I need to check my schedule or anything.

Claire: How do you feel?

Catherine: Physically? Great. Except my hair seems kinda unhealthy, I wish there was *something* I could do about that.

Claire: Mitch has become an excellent cook. It's like his hobby now. He buys all these gadgets, garlic, press, olive oil spread, every night there's something new. The other day he made the best vegetarian chili.

Catherine: What *are* you talking about?

Hal: It's not what your dad did.

Catherine: I think it was in a way. I mean, he'd attack a problem from the side, you know, from some weird angle. Sneak up on it, grind away at it.

When your dad was younger than both of us, he made major contributions to three fields! Game theory, algebraic geometry, non-linear operators... Look, if I came up with one tenth of the shit your dad produced, I could write my ticket to any math department, in the country.

[Reading Robert's notebook] "Talking with students helps, writing in buses. Most of all, Kathy. Her refusal to let me be institutionalised, caring for me herself, has certainly saved my life. Made writing this possible, made it possible to imagine doing math again. Where does her strength come from? I can never repay her. Today is her birthday, she is 24. I'm taking her to dinner."

I always liked you. But then I thought, no, you don't flirt with your doctoral advisor's daughter.

I want to stay here with you. I want to spend the day with you. If at all possible, I want to spend as much time as I can, unless I'm coming on way too strong right now and scaring you, in which case I'll begin backpedalling immediately.

It's a, a result, a proof. I mean, it looks like a proof - I mean, it IS a proof, a very long proof, I haven't read through it all yet, or checked it, I mean, I don't even know if I could check it... if it's a proof of what I think it's a proof of, it's a very important proof.

Here's my suggestion, alright. I know three or four guys at the department, very sharp, disinterested people who knew your dad, knew his work. Let me take this to them, I'll tell them that we, we found something, something potentially major, we're not sure of the authorship, I'll sit down with them, we'll talk through it carefully, and then we'll figure out what we've got.

I think the first thing I'm going to do is throw her in the shower and get her into the sun.

It's a funeral, but we don't have to be completely grim about it!

Mitch has become an excellent cook. It's like his hobby now. He buys all these gadgets, garlic, press, olive oil spread, every night there's something new. The other day he made the best vegetarian chili.

Claire: I thought we'd have some people over tonight. If you're feeling OK.

Catherine: It's like a monkey at a typewriter. A hundred and three notebooks full of bullshit.

Hal: I'm prepared to look at every page. Are you?

Catherine: No. I'm not crazy.

Hal: Well, I'm gonna be late. Uh, some friends of mine are in this band. They're playing in a bar on Diversey, way down the bill. They go on about 2 to 2:30. I said I'd be there.

Catherine: Great.

Hal: They're all in the math department, they're really good. They have this song called "i", you'd like it, lower-case i, they just stand there and don't play anything for three minutes.

Catherine: Imaginary number.

Hal: It's a math joke ... you see why they're way down on the bill.

Catherine: That's a long drive to see some nerds in a band.

Hal: You know, I hate when people say that. It's not really that long of a drive.

Catherine: So, they are nerds.

Hal: Oh, they're raging geeks. But they're geeks who, you know, can dress themselves and hold down a job at a major university. Some of them have switched from glasses to contacts. They, uh, play sports, they play in a band, they get laid suprisingly often, so it makes you kinda question the whole set of terms. Geek, nerd, wonk, dilbert, paste eater ...

Catherine: You're in this band, aren't you.

Hal: Ok, yes. I play the drums. You wanna come? I never sing, I swear to God.

Catherine: Still making those lists?

Claire: Oh, it's a compulsion.

Catherine: Do you ever cheat and tick off something you haven't actually done yet?

Claire: It makes my hair look, smell and feel good, and that is the extent of my information about it. You might like it if you decide to use it.

Catherine: Thanks. I'll try it.

Claire: Were you abusive?

Catherine: This one cop who keep spitting on me when he talked. It was disgusting!

Claire: Did you use the word "dickhead"?

Catherine: Guh, I don't remember!

Claire: Did you tell one cop to go ... have sex with the other cop's mother?

Catherine: No!

Claire: That's what they said.

Catherine: Not ... with that phrasing.

Claire: Did you strike one of them?

Catherine: They were trying to come into the house ...

Claire: Oh!

Catherine: ... I may have pushed him a little.

Hal: You look great.

Catherine: Clare gave it to me.

Hal: I ... I like it.

Catherine: It doesn't really fit.

Hal: Sure it does.

Catherine: You can't prove it.

Hal: Well, I could and try and disprove the opposite. I can prove that it doesn't not fit.

Catherine: How?

Hal: I could take a vote.

Hal: Mathematicians are insane. I went to this conference in Toronto last fall, I have never been so exhausted in my life. 48 straight hours of partying, drinking, drugs, papers, lectures ...

Catherine: Drugs?

Hal: Amphetamines, mostly. I mean, I don't, but some of the older guys are really hooked. They think they need it.

Catherine: Why?

Hal: I guess there's this fear that your creativity peaks around twenty three, and then it's all downhill from there.

Catherine: That's what my dad thought.

Hal: I guess, all the really original work, it's all young guys.

Catherine: Young guys?

Hal: I mean, no, there are some women.

Catherine: Really, who?

Hal: Err, there's a woman at Stanford, I can't remember her name.

Catherine: Sophie Germaine?

Hal: Yeah,. I think I've seen her at meetings, but I don't think I've ever met her.

Catherine: She was born in Paris in 1776.

Hal: Then I've definitely never met her.

Hal: Germaine primes. Like, double them and add one, you get another prime. Like, two is prime. Double plus one is five, also prime.

Catherine: Right. Or 92,305 × 216,998 plus one.

Hal: ... Right.

Clare: What does it mean?

Hal: It means that, during a time when everyone thought your dad was crazy, he was doing some of the most important mathematics in the world. If it checks out, it means you publish instantly, it means you hold press conferences, it means that all newspapers around the world are going to want to talk to the person who found this notebook.

Clare: Catherine.

Hal: Catherine.

Catherine: I didn't find it.

Hal: Yes, you did.

Catherine: No, I didn't.

Clare: Well, did you find it, or did Hal find it?

Hal: Well, I didn't find it.

Catherine: I didn't find it. I wrote it.

Clare: So, you wrote this incredible thing, but you didn't tell anyone?

Catherine: I'm telling you both now.

Clare: Catherine, I'm sorry, but I find this very hard to believe. This is dad's handwriting.

Robert and Catherine: ... as the sum of two cubes in two different ways.

Robert: 123 + 13 = 1729.

Catherine: And 103 + 93. Yes, we've got it, thank you.

Robert: You see? Even your depression is mathematical. Stop moping. [hands her a notebook] Do some work.

Catherine: You have the book, she told me that she gave it to you, so, do whatever you want with it. Publish, go for it, have a press conference. Tell the world what my father discovered.

Hal: I don't think your father wrote it.

Catherine: You thought so last week.

Hal: That was last week. I spent this week reading the proof. I mean, I think I understand it more or less, it uses a lot of newer mathematical techniques, things that were developed in the 80s and 90s. Non-communicative geometry, random matrices. I think I learned more mathematics this week than I did in three years of grad school!

Catherine: So?

Hal: So the proof is very ... hip.

Catherine: Get some sleep, Hal.

Hal: What was your father doing these last twenty years? He wasn't well, was he?

Catherine: Are you done?!

Hal: I don't think he would have been able to master those new techniques.

Catherine: He was a genius!

Hal: But he was nuts.

Catherine: So, he read about them later.

Hal: Maybe, the books he would have needed are upstairs, in your room, some of them. He dated everything. Even in his most incoherent entries, he dated. There are no dates in this.

Catherine: The handwriting ...

Hal: Parents and children sometimes have very similar handwriting, especially if they've spent a lot of time together.